Normal map looking weird on mesh
I was struggling days to find out what caused the problem with baking normal maps and think I found a nice solution. I could have used much easier way to bake normal maps for my mesh.
To bake normal map for my mesh, I needed to do the following:


Have only one mesh for baking normal map
Use multires modifier on that object
Raise the levels of subdivisions as high as I need to have nice details
Once I've created details in sculpt mode, go to Cycles Render Engine
Go to "Render" tab and open "Bake" option 
Make sure that "Selected to Active" is disabled (becaused baking normal maps with this option is based on other method)
Change "Bake Type" to "Normal"
Hit the "Bake" button and be happy to have good normal map.


This way of baking normal maps for mesh is usually used when your mesh has fine topology (the mesh consists of square-shaped faces and not triangles), because multires modifier will subdivide all faces and mesh that consists of triangles, will deform the mesh alot. However, it's easier to subdivide squares and it doesn't cause any problems this way.